1/cos2x+tan2x=(1+sin2x)/cos2x
=(sin²x+cos²x+2sinxcosx)/(cos²x-sin²x)
=(sinx+cosx)²/[(cosx+sinx)(cosx-sinx)]
=(sinx+cosx)/(cosx-sinx)
=(tanx+1)/(1-tanx)
=2008
sinx+siny=sin225°=sin(180°+45°)=-sin45°=-√2/2
cosx+cosy=cos225°=cos(180°+45°)=-cos45°=-√2/2,
那么(sinx+siny)²=sin²x+2sinxsiny+sin²y=1/2
(cosx+cosy)²=cos²x+2cosxcosy+cos²y=1/2
两式相加,得：1+1+2(cosxcosy+sinxsiny)=1
那么2+2cos(x-y)=1
所以cos(x-y)=-1/2